Re: Define the intersection points of polynomials

Was anyone else able to provide a solution?

My point is no solution could be found in other set other than the reals.

When we started you convinced me there were many such solutions so all I had to do was find one that did not work. As I began solving these I began to think there were not many solutions. Now, I do not believe there is even one such solution.

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.

Re: Define the intersection points of polynomials

Broadly speaking, the field in which we are operating influences the answer to the question of whether a system of equations has solutions or not to some extent, but not in the ways that the OP thinks it does. Whether we are operating in a prime field or an extension of a prime field (what the OP calls gf or GF) has relatively little to do with the matter. In particular, for linear equations, the general theory of linear equations over a field usually has more to say about the matter than the identity of the field.

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.

Re: Define the intersection points of polynomials

You chose negative integers that they do not exist in GF.

I did not choose anything that is what the multiplications from your formula produced. I asked what you wanted to do next on those coefficients. I would have used a modulo on them to bring them into the set. You had no answer.

You controlled the data as they were integers.

Your set or any prime field is nothing but a subset of the integers. If there was no intersection over the integers how can there be one over a subset of the integers?

I have recommended to you a site where they would further answer your questions. They provided no solution either. Maybe there isn't one! This is the possibility you keep avoiding.

I have asked you to produce any solution or to have your author produce one. I would like to see it.

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.

Re: Define the intersection points of polynomials

I used the field 2^128 and also polynomial representation basis. Therefore, addition multiplication and division is not defined as it were on real numbers. I have tested it many times that these operations never return negative elements. It is not possible.

In math stack they all said that the first problem where linear equation are empolyed, there is a solution on GF. Do you think that you can solve it?

My problem is that I dont have an algorithm to solve the second problem. I have the definitions of the operations but I

cannot solve a system of 4 equations with 4 unknowns. I am not sure that there is a solution but I think tha there is. I do

I do not avoid any possibility but I think that believing that there is no solution is the easy but unhopefully the wrong way.

Re: Define the intersection points of polynomials

Ok. I understand that I can not give you clear answers because I also do not understand many things.

I thought that you read my post where this set was described in detail and the solution is provided by another user user. This is a system of 2 linear equations. If we want to be mathematically correctly there is no geometrical representation of this problem in the GF.

Re: Define the intersection points of polynomials

They are advanced in mathematics. The know that if theory is correct, numbers are never a problem.

That is what they teach in school and it is the biggest myth in the entire world. There are many cases where theory does not match the numbers. Theoreticians can not get numbers! Computational people can! Math is split into pure and applied and they do not even speak the same language.

Now, to have any hope of doing one of these in a convincing way the field will have to be smaller than 2^128. These are 40 digit numbers, too big for a test.

In mathematics, you don't understand things. You just get used to them.If it ain't broke, fix it until it is.No great discovery was ever made without a bold guess.

Re: Define the intersection points of polynomials

In order to be sure that the system has a solution I construt the system of equations to have a common point the x0 y0. i.e. I define the intersection point x0y0 and then I pretend that I do not know it..

That was the problem I posted yesterday. But in that problem the eq. were quadratics...So I used to construct it, two points x0x1 y0 y1. Then by knowing M1..M4 and the four unique X2 y2 for each polynomial andby pretending that you dont know the x0x1 y0 y1 you had to solve the system.You said the system that hadn t got a solution in GF. As i have constructed the system I was sure that a solution existed.Thats why I was sure that the system has a solution!!!! Because I knew the solution.